You might try re-ripping the CD directly to AAC to see if better results.

Or try another app. I just converted three gapless FLAC tracks from DSOTM to AAC (QAAC) and MP3 (LAME) using foobar2000. Both play back gapless -- or so close I can't hear it -- in foobar2000. It's possible they would not do so if played back in another app or on a portable player. Not much you can do about that other than combine all the tracks into one big file and, if your player supports it, use a CUE sheet to index tracks.

The MP4 (.m4a) container has two different options for gapless playback; the ISO standard, and Apples "iTunes" implementation.

I think dBPowermp uses the FDK-AAC encoder by default, which has the ability to write either or both options when using the fdkaac frontend (using the "-G" option)... I'm not sure if the dBPoweramp GUI exposes this functionality to the user, but it might be worth investigating. Otherwise JunkieXLs suggestion of converting to ALAC then AAC with Apple tools seems a good idea.